Solve 8x^2+4+11x^2-20

$$8 x ^ { 2 } + 4 + 11 x ^ { 2 } - 20$$

Evaluate

$$19x^{2}-16$$

Solution Steps

Combine 8x^{2} and 11x^{2} to get 19x^{2}.

$$19x^{2}+4-20$$

Subtract 20 from 4 to get -16.

$$19x^{2}-16$$

Differentiate w.r.t. x

$$38x$$

Steps Using Derivative Rule for Sum

Combine 8x^{2} and 11x^{2} to get 19x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(19x^{2}+4-20)$$

Subtract 20 from 4 to get -16.

$$\frac{\mathrm{d}}{\mathrm{d}x}(19x^{2}-16)$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$2\times 19x^{2-1}$$

Multiply 2 times 19.

$$38x^{2-1}$$

Subtract 1 from 2.

$$38x^{1}$$

For any term t, t^{1}=t.

$$38x$$